Master Stephanus Concordance

Cross-Corpus Reconciliation Across Euclid, Elements, Proclus, Aristotle, Hoenen & Pacioli

This concordance reconciles every plato:* citation across the six sister repositories of the GEOMETOR Digital Scriptorium (36 canonical citation keys spanning 58 repository-level declarations and 63 apparatus files in geometor/euclid, geometor/elements, geometor/proclus, geometor/aristotle, geometor/hoenen, and geometor/pacioli) directly to synchronized Stephanus anchors in Loci Mathematici et Geometrici.

Primary Mathematical & Philosophical Loci (Staged Verbatim in Units I–VI)

Sister Citation Key	Sister Repos	Stephanus Locus	Codex Target	Mathematical & Noetic Context
plato:meno:76A	euclid, elements	75d–76a	Meno 75d–76a	Euclid Elements I, Defs. 13–14 & Proclus Friedlein 136–143: figure (schema) defined as limit of solid (stereou peras).
plato:meno	aristotle	80d–86c	Meno 80d–86c	Aristotle Anal. Post. I.1 (71a29) & Anal. Prior. II.21 (67a21): Meno’s paradox of inquiry resolved via universal vs. particular recognition.
plato:meno:81e-85d	proclus	81e–85d	Meno 81e–85d	Proclus In Euclidem Prologue I (Friedlein 45.15–46.3): mathematical recollection (anamnesis) awakened through diagrammatic discovery.
plato:meno:82b-85b	hoenen	82b–85b	Meno 82b–85b	Hoenen De Noetica Geometriae Cap. I & VII: intellectual insight (intuitus mentis) into the necessary nexus Q = 4 + 4 = 8 in the singular diagram.
plato:theaetetus	euclid, elements	147c–148b	Theaetetus 147c–148b	Euclid Elements Book X Introduction (Heath Vol. III, pp. 1–4): historical origin of the theory of irrationals in the Academy.
plato:theaetetus:147.d	euclid, elements	147d	Theaetetus 147d	Euclid Elements X, Defs. 1–4: commensurable in length (mekei) vs. commensurable in square/power only (dynamei).
plato:theaetetus:147D	euclid, elements	147d	Theaetetus 147d	Euclid Elements X.9 & Scholium: Theodorus’s individual proofs from 3 to 17 square feet generalized by Theaetetus.
plato:theaetetus:147.d.sqq	euclid, elements	147d–148b	Theaetetus 147d–148b	Euclid Elements VII, Defs. 16–19: plane, equilateral square (isos isakis), and oblong (promekes) numbers.
plato:theaetetus:147-e-148-b	euclid, elements	147e–148b	Theaetetus 147e–148b	Euclid Elements X.9: exact number-theoretic criterion for rational lengths (meke) vs. quadratic surds (dynameis).
plato:rep	euclid, elements	VI 509d–511e; VII 525a–534e	Republic VI 509d–511e; VII 525a–534e	Euclid Elements Vol. I Ch. IX: Plato’s philosophy of mathematical hypotheses, definitions, and deductive method.
plato:republic	aristotle	VI 509d–511e; VII 525a–534d	Republic VI 509d–511e; VII 525a–534d	Aristotle Metaphysics B.2, M.1–3 & Anal. Post. I.10: mathematical intermediates (ta mathematika), dianoia, and unhypothetical first principles.
plato:rep:VI.510b-511d	proclus	VI 510b–511d	Republic VI 510b–511d	Proclus In Euclidem Prologue I (Friedlein 10.15–11.25, 29.14–32.20): dianoia as the proper cognitive faculty of geometry between nous and opinion.
plato:rep:VI.510C	euclid, elements	VI 510c	Republic VI 510c	Euclid Elements I, Defs. 10–12: geometers hypothesize the odd and even, the figures, and the three species of angles (right, obtuse, acute).
plato:rep:VI.510c	hoenen	VI 510c–511a	Republic VI 510c–511a	Hoenen De Noetica Geometriae Cap. I: geometers use visible figures as images while reasoning about the square itself and the diagonal itself.
plato:rep:VII.525a-534e	proclus	VII 525a–534e	Republic VII 525a–534e	Proclus In Euclidem Prologue I (Friedlein 20.8–24.20, 35.17–42.8): the five mathematical sciences as the cathartic ascent to dialectic.
plato:rep:528.b.d	euclid, elements	VII 528b–d	Republic VII 528b–d	Euclid Elements Book XI Introduction: Plato’s programmatic critique of leaping from plane geometry to astronomy before cultivating 3D stereometry.
plato:rep:VII.532c	hoenen	VII 532c	Republic VII 532c	Hoenen De Noetica Geometriae: liberation of the eye of the soul from sensible shadows through mathematical arts.
plato:rep:VII.533c	hoenen	VII 533c	Republic VII 533c	Hoenen De Noetica Geometriae: geometry dreams about being so long as it leaves its hypotheses unmoved without ascending to the unhypothetical.
plato:timaeus:31c-36d	proclus	31c–36d	Timaeus 31c–36d	Proclus In Euclidem & In Timaeum: geometric analogia as the fairest cosmic bond and harmonic constitution of the World-Soul.
plato:timaeus:32-a-b	euclid, elements	32a–b	Timaeus 32a–b	Euclid Elements VIII.11–12: one mean proportional suffices between two square/plane numbers, whereas two means are required between solid cubes.
plato:timaeus:32-a-sqq	euclid, elements	32a–c	Timaeus 32a–c	Euclid Elements VIII.11–12 & V, Def. 9–10: duplicate and triplicate ratios of plane and solid numbers.
plato:timaeus:32.a.b	euclid, elements	32a–b	Timaeus 32a–b	Euclid Elements VIII.11–12: architectural necessity of four elements (fire, air, water, earth) from double geometric means.
plato:timaeus	euclid, elements, aristotle	31b–36d, 53c–56c	Timaeus 31b–36d, 53c–56c	Euclid Elements Book XIII & Aristotle De Caelo III.7–8 (306a1–307b18): resolution of elemental bodies into planar right triangles.
plato:timaeus:53c-56c	pacioli	53c–56c	Timaeus 53c–56c	Luca Pacioli De Divina Proportione (1509, 9 citations across Caps. V, XXV–LV): the five regular Platonic bodies assigned to fire, earth, air, water, and the cosmos.
plato:timaeus:54-d-e	euclid, elements	54d–e	Timaeus 54d–e	Euclid Elements XIII.13–17: six 1:sqrt(3):2 half-equilateral scalene triangles compose each equilateral cosmic face.
plato:parm:137E	euclid, elements	137e	Parmenides 137e	Euclid Elements I, Def. 4 & Def. 15: Plato’s optical definition of the straight line (‘middle blocks both extremes’) and equidistant circle.
plato:parmenides:137e	proclus	137e	Parmenides 137e	Proclus In Euclidem (Friedlein 109.21–110.16): commentary on Plato’s optical characterization of straightness vs. Euclid I, Def. 4.
plato:parm:145B	euclid, elements	145a–b	Parmenides 145a–b	Euclid Elements I, Defs. 13–14: figure (schema), beginning, middle equally distant from extremes, round, straight, or mixed.
plato:philebus:16c-26d	proclus	16c–26d	Philebus 16c–26d	Proclus In Euclidem Prologue I (Friedlein 5.18–7.12): Limit (peras) and Unlimited (apeiron) as supreme ontological principles of geometry.
plato:laws:817.e	euclid, elements	VII 817e–820d	Laws VII 817e–820d	Euclid Elements Book X & Book VII: three liberal mathematical sciences and the scandal of ignorance regarding incommensurable lengths, surfaces, and solids.

Peripheral Civic & Optical Loci (Catalogued in Critical Notes)

Six peripheral citations in Heath’s philological notes and Hoenen’s civic-number excursus fall outside the mathematical dialogues proper and are analyzed in the corresponding Critical Notes tracks:

Sister Citation Key	Sister Repos	Stephanus Locus	Scope & Analytical Note Location
plato:leges:737e-738b	hoenen	Laws V 737e–738b	Hoenen De Noetica Geometriae Cap. IV: civic number 5,040 (= 7!) divisible by every integer from 1 to 10 (59 proper divisors); analyzed in Unit III Notes. (Unit III — Republic VI–VII: The Divided Line, Dianoia & the Quadrivium — Critical Commentary & Notes)
plato:leges:738a	hoenen	Laws V 738a	Hoenen De Noetica Geometriae Cap. IV: Plato’s exact divisor theorem for 5,040 (divisible by 1..12 except 11, which divides 5,038); analyzed in Unit III Notes. (Unit III — Republic VI–VII: The Divided Line, Dianoia & the Quadrivium — Critical Commentary & Notes)
plato:laws:777D	euclid, elements	Laws VI 777d	Heath on Euclid Common Notion 3: Plato’s proverbial ‘if equals be added to unequals, the wholes remain unequal’; contextualized in Unit VI Notes. (Unit VI — Parmenides, Philebus & Laws VII: Straightness, Limit & Incommensurability — Critical Commentary & Notes)
plato:rep:417	euclid, elements	Republic III 416d–417b	Peripheral civic reference in Heath’s philological notes on terminology; outside mathematical curriculum. (Unit III — Republic VI–VII: The Divided Line, Dianoia & the Quadrivium — Critical Commentary & Notes)
plato:rep:X.602c	euclid, elements	Republic X 602c–603a	Heath on Optics & Measurement: bent-stick refraction illusion overcome by numbering, measuring, and weighing (metretike); analyzed in Unit VI Notes. (Unit VI — Parmenides, Philebus & Laws VII: Straightness, Limit & Incommensurability — Critical Commentary & Notes)
plato:sophist:235.d	euclid, elements	Sophist 235d–236c	Heath on Perspective Optics (scenographia): true symmetry (eikastike) vs. foreshortened optical appearance (phantastike); analyzed in Unit VI Notes. (Unit VI — Parmenides, Philebus & Laws VII: Straightness, Limit & Incommensurability — Critical Commentary & Notes)